The lines with equations:
y = x + 1,
y = mx − 1,
& y = −4x + 2m
pass through the same point.
Determine all possible values for m.
This is really just a system of three equations in 3 unknowns.
Equate the first and second and solve for x:
x=2/(m1)
Equate the first and third and solve for x:
x=(2m1)/5
Equate these two and solve for m:
0=m^2  3m  9
0=(2m+3)(m3)
The solutions are
m=3/2 or m=3
The corresponding intersection points are (4/5,1/5) & (1,2) respectively.
Graphing the equations in the xy plane with m an animated parameter is interesting to watch. One line stays still, one slides up or down, one tilts to meet them on either side.

Posted by Jer
on 20180107 12:29:31 